Anastasia was born on September 24, 1981, in Moscow. As a child, she dreamed of becoming a journalist and even prepared to enter the journalism faculty by attending the School of Young Journalists at the Faculty of Journalism at Moscow State University. But at the last moment, she changed her mind and decided to enter the theater. Her first attempt was unsuccessful—Tsvetaeva was not accepted as an actress. However, Anastasia did not give up and was accepted on her second attempt in 2000 at the Russian Academy of Theatre Arts (GITIS) in Vladimir Andreev's course. Her movie debut took place while she was still a first-year student. Director Denis Yevstigneyev cast the freshman in a small episode of his comedy "Let's Make Love" (2002), where Tsvetaeva played a prostitute. The following year, Tsvetaeva starred in another youth comedy by 31-year-old debut director Ruslan Baltzer, "Don't Even Think" (2003), where she played a wild beauty planning a criminal scheme with her fun-loving friends.
The actress then reprised her role in the sequel "Don't Even Think 2: Shadow of Independence" (2004).
However, it was not these comedies that brought her widespread popularity, but a music video. In 2003, 22-year-old Tsvetaeva appeared in a video for the famous band "Zveri" for the song "Everything That Concerns." This small work significantly increased her fan base among young audiences. Her success among teenagers was solidified by her role in Ilya Khotinenko's comedy "Call Me Genie" (2005), where Tsvetaeva played in a duet with Pyotr Buslov. Around this time, the actress divorced her first husband, with whom she had lived for five years.
The actress is dating director Oleg Goncharov and continues her career by solidifying her image as a "star of youth movies": she starred in the lead role in the series "Young and Happy" (2005), which tells the classic plot of a provincial girl coming to Moscow and encountering both swindlers and the collapse of her hopes. However, the role turned out to be prophetic—in this project, Tsvetaeva's character gives birth to a son, and in real life, Tsvetaeva also becomes a mother. She has a son, Kuzma, with director Oleg Goncharov. According to the actress, after the birth of her child, a "turning point" occurs in her life—she now refuses "frivolous roles in youth movies and tries to present her image as more mature and dramatic." Although judging by her filmography, this is difficult to achieve—her arsenal of roles continues to be filled with not the most "heavy" movies like "Masha and the Sea" (2008), "Smart and Beautiful" (2009), "Melody of Love" (2010), and others.
Five years after the birth of her son, 29-year-old Anastasia marries Israeli businessman Nadav Olgan, whom she met at a disco in Turkey. "The whole beginning of our romance is one fateful coincidence. We met in Turkey, at a hotel where Nadav was celebrating the Jewish New Year with his company, and I was celebrating my birthday with friends. And quite by chance, he had to stay in the honeymoon suite. That was the first sign," Anastasia admits. Two years later, the couple had a daughter, Esther.
The Russian actress admits that she lives between Moscow, where she continues to act in movies, and Tel Aviv, where she lives with her family.
Alongside filming, the actress is involved in creating her own jewelry, which she sells online, writes articles for glossy magazines, maintains a personal blog on the internet, and communicates with her clients—buyers of her jewelry.